Are we integrating with respect to x or t? I suspect you mean for the two variables to be the same, and if so, let u be the value under the radical, and you will find you can easily get du as part of the integral.
If you are unsure of your result, use differentiation to check your result:
We can see it is close (essentially the wrong constant factor of the radical), but not quite right. I would let:
and so we have:
Now, checking by differentiation, we find:
The derivative of the anti-derivative is the original integrand, so our result is correct.